Question

Are all quadratic equations functions?

Answer 1

When you have a fucntion like \[y=ax^2+bx+c\]the expression\[ax^2+bx+c\]is a quadratic expression and is called the rule of association for the fucntion. Any time you have a quadratic expression using the x-variable set equal to to y, it is a function.
(continued)

Answer 2

if on the other hand, you have say\[x=y^2\]you do not have function in which the x-variable is the domain variable.

Is this along the line in which you were asking the question?

Answer 3

if it's y equals x-squared, then its a fucntion
if it's x equals y-squared, then it is not a function